The publication is a dependable reference for mathematicians and researchers interested in stochastic integrals. The manuscript takes a look at equations in canonical form, as well as justification of the canonical extension in stochastic modeling rate of convergence of approximations to solutions comparison of ordinary and stochastic differential equations and invariance under change of coordinates. The book then examines stochastic differential equations, including existence of solutions of stochastic differential equations, linear differential equations and their adjoints, approximation lemma, and the Cauchy-Maruyama approximation. Discussions focus on differentiation of a composite function, continuity of sample functions, existence and vanishing of stochastic integrals, canonical form, elementary properties of integrals, and the Itô-belated integral. The publication first ponders on stochastic integrals, existence of stochastic integrals, and continuity, chain rule, and substitution. This means that, for $s < t$, $s,t\in$, that $B(t)-B(s)$ is normally distributed with mean zero and variance $t-s$.Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Calculus and Stochastic Models focuses on the properties, functions, and applications of stochastic integrals.
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